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Wednesday, April 14, 2021

What is the fastest car in the world?


In the article, no answer is given to the question from the title. The title serves as an example of a problem that cannot be sufficiently solved, and as such, it may and will lead to endless discussions.

Similarly, we cannot reliably decide whether Windows or Linux rules or whether the latest U.S. presidency candidate outmatches the previous one.

At best, the debates on given topics may lead to the enlightenment of participating parties, given they care about learning, which is seldomly the case.

(Still, catfights between die-hard fans may inspire sociologists or psychologists to publish new studies on damnable human nature.)

Since this article intends to focus on problem-solving, the output does not deal with answers; the output outline more questions to ask when dealing with unknown problems.

So what about the fastest car in the world?

First of all, the task seems rather vague. Do we even know what does it mean fastest? What does it mean car? What does it mean world?

What about a car, loaded in a spacecraft, flying to Mars? There is no doubt that such a vehicle moves fast, but no one would probably feel satisfied with such a winner.

The common opinion would express a counter-argument in the following fashion, "Geesh, everybody knows what a car is. There is no need to define such elementary stuff."

Unfortunately, for the rigorous and correct answer, the definition of the examined car is essential. Besides ordinary four-wheeled cars, the world offers high-tech race vehicles or even specially designed speed-record-attacking cars that drive flat and straight surfaces of salt deserts.

So, what defines our car? What if the rocket is attached to its roof, overcoming all speed limits and serving as a one-way suicide instrument as was already tested by one crafty madman?

Moreover, the external conditions should be taken into calculations. In theory, people can build a long vacuum tunnel with a perfect road; in afterthought, the artificial environment may hugely affect the experimental results.

The possibilities are endless, at least on paper. In real life, no one would take them into account.

But since people cannot distinguish between feasible and impossible, everyone puts one's bottom line differently.

There is much more to say on the topic, but the message is clear. Without exact boundaries, no one can confidently decide what the fastest car in the world is.

What people take for granted is, more often than not, just a misunderstanding. For instance, is jumping to water safe? See, another question with no good answer.

Of course, children keep jumping into the water all day, and their parents do not mind. But what if the water were frozen?

"But typically, water exists in a liquid state!"

Says who? Certainly not the Eskimos.

For a general audience, such a rebuttal feels like trolling, but correct thinking requires a meticulous mindset.

With too loosened boundaries, the solution may be incorrect in edge cases, which, no matter how unlikely, will backfire eventually. The famous Murphy's laws cover it.

Murphy's First Law: Anything that can go wrong will go wrong.

Now, from the mathematical perspective, every problem fits a simple line:

input -> output

With knowledge of all necessary values that affect results (no less, no more) and with a function that maps the input into correct output, no unsolvable problem exists.

If the opposite situation happened and the Universe was based, somewhere deep inside, on randomness, then all science would be shaken, and unpredictable magic would rule the world.

Thus, every problem needs to define a complete set of input parameters. If one is missing, the function does not guarantee the referential transparency - i.e., for the same input, we can obtain different outputs.

Now, when encountered a task, not solved before, the methodology consists of simple recursive steps:

1. Can the problem be solved?
2. If not, divide it into smaller parts!
3. Can the smaller part be solved?
4. If not, bring it to line 2!
5. If yes, return the solution!

Obviously, the problem lacks a solution when some of its parts cannot be broken down into smaller, solvable chunks. Such a situation represents the limit of human technology.

On the other hand, note that problems overlapping the reasonable frame of human computing capacity are solvable, even though they last millions of years to compute.

As aforementioned, to decide which car is the fastest in the world, the experimental race needs precise specifications. And even then, we can conclude that the final result guarantees certain correctness only under these specifications.

For instance, if the experiment's temperature is set to 20°C, the winning car at -20°C may or may not stay the same.

But not only that! When taken into consideration the complexity of the physical world and our inability to measure all variables properly, we should not take our results for granted.

What if one of participating cars performed sub-optimally due to an error of a driver or maintenance technician?

With such a level of uncertainty, people are doomed to express their opinions rather hesitantly; those who claim to know something for sure may be proved wrong anytime.

The more complex is the problem we need to solve, the more unexpected events may happen. Realizing this, we can safely predict that anything, no matter the estimated reliability, can go south eventually.

Even being sure at 99.99% that we did everything as safe as possible, the remaining 0.01% of mistakes can and will undermine our efforts, especially after a sufficient amount of repetitions. This is why cybersecurity never works and why software has bugs.

In our case, when dealing with the fastest car problem, we should repeat our measurements several times to obtain a good statistical sample. And of course, we need to run the experiments under the same conditions.

From a practical point of view, performing the whole thing correctly would require so much effort and money that we can safely dismiss this as an impossible task.

So we will never know what the fastest car in the world is.